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Masteriza [31]
2 years ago
6

Remember to show work and explain. Use the math font.

Mathematics
1 answer:
vichka [17]2 years ago
7 0

Answer:

\large\boxed{1.\ f^{-1}(x)=\sqrt[12]{3^x}}\\\\\boxed{2.\ f^{-1}(x)=\sqrt[4]{3^x}}\\\\\ \boxed{3.\ f^{-1}(x)=\sqrt[3]{4^{7-x}}}

Step-by-step explanation:

(a^n)^m=a^{nm}\\\\\log_ab=c\iff a^c=b\\\\a^{\log_ax}=x\\\\n\log_ab=\log_ab^n\\\\\log_ab+\log_ac=\log_a(bc)\\============================\\\\1.\\y=3\log_3x^4\to y=\log_3(x^4)^3\to y=\log_3x^{12}

2.\\y=\log_3x^4\\\\\text{Exchange x and y. Solve for y:}\\\\\log_3y^4=x\Rightarrow3^{\log_3y^4}=3^x\Rightarrow y^{4}=3^x\\\\y=\sqrt[4]{3^x}\\-------------------------

3.\\y=-\log_4x^3+7\\\\\text{Exchange x and y. Solve for y:}\\\\-\log_4y^3+7=x\qquad\text{subtract 7 from both sides}\\\\-\log_4 y^3=x-7\qquad\text{change the signs}\\\\\log_4y^3=7-x\Rightarrow4^{\log_4y^3}=4^{7-x}\\\\y^3=4^{7-x}\Rightarrow y=\sqrt[3]{4^{7-x}}

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Explain why 6^3x7^3=42^3 is correct.
Orlov [11]

Answer:

{6}^{3} \times {7}^{3}  =  {(6 \times 7)}^{3}  =  {42}^{3}

Step-by-step explanation:

When two or more quantities have the same exponents, their bases can be multiplied together.

4 0
3 years ago
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A box of 25 munchkins cost $5.46 what is the unit rate per munchkin
timurjin [86]

The unit rate per munchkin is $0.22.

<h3>What is Division?</h3>

Division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.

The cost of 25 munchkins cost $5.46, therefore, the unit rate of each munchkin can be written as,

\text{Cost of unit munchkin} = \dfrac{\text{Total cost of munchkins}}{\text{Number of munchkins}}\\\\\text{Cost of unit munchkin} = \dfrac{\$5.46}{25}=\$0.2184 \approx \$0.22

Hence, the unit rate per munchkin is $0.22.

Learn more about Division:

brainly.com/question/369266

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5 0
2 years ago
Jeremy's score was 1.75 standard deviations above the mean. which kf thr following is closest to his percentile rank
Gelneren [198K]
The answer is 96%.

Explanation:
It is generally presumed that the scores are normally distributed.

1) You are given how many standard deviations from the mean Jeremy's score is. This is exactly the definition of the z-score. Therefore z = 1.75

2) Look at a left-tail z-table in order to find the area of the normal curve on the left of your z-score (see picture attached). A = 0.9599

3) Multiply the area by 100 in order to find the percentile:
<span>0.9599 </span>× 100 = 95.99
Therefore, 95.99% of the students scored less than Jeremy.

Hence, the answer is 96%.

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